Hands-on Exercise 2-1 & 2-2

First-order Spatial Point Patterns Analysis Methods

1.Installing and Loading the R packages

pacman::p_load(sf, terra, spatstat, 
               tmap, rvest, tidyverse)

2.Importing and Wrangling Geospatial Data Sets

mpsz_sf <- st_read("data/MasterPlan2019SubzoneBoundaryNoSeaGEOJSON.geojson") %>% 
  st_zm(drop = TRUE, what = "ZM") %>% st_transform(crs = 3414)

Reading layer `MasterPlan2019SubzoneBoundaryNoSeaGEOJSON' from data source 
  `C:\Sathvika-7284\ISSS626-geo\Hands-on_Ex\Hands-on_Ex02\data\MasterPlan2019SubzoneBoundaryNoSeaGEOJSON.geojson' 
  using driver `GeoJSON'
Simple feature collection with 332 features and 2 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

extract_kml_field <- function(html_text, field_name) {
  if (is.na(html_text) || html_text == "") return(NA_character_)
  
  page <- read_html(html_text)
  rows <- page %>% html_elements("tr")
  
  value <- rows %>%
    keep(~ html_text2(html_element(.x, "th")) == field_name) %>%
    html_element("td") %>%
    html_text2()
  
  if (length(value) == 0) NA_character_ else value
}

mpsz_sf <- mpsz_sf %>%
  mutate(
    REGION_N = map_chr(Description, extract_kml_field, "REGION_N"),
    PLN_AREA_N = map_chr(Description, extract_kml_field, "PLN_AREA_N"),
    SUBZONE_N = map_chr(Description, extract_kml_field, "SUBZONE_N"),
    SUBZONE_C = map_chr(Description, extract_kml_field, "SUBZONE_C")
  ) %>%
  select(-Name, -Description) %>%
  relocate(geometry, .after = last_col())

mpsz_cl <- mpsz_sf %>%
  filter(SUBZONE_N != "SOUTHERN GROUP",
         PLN_AREA_N != "WESTERN ISLANDS",
         PLN_AREA_N != "NORTH-EASTERN ISLANDS")

write_rds(mpsz_cl, 
          "data/mpsz_cl.rds")

childcare_sf <- st_read("data/ChildCareServices.geojson") %>% 
  st_zm(drop = TRUE, what = "ZM") %>%
  st_transform(crs = 3414)

Reading layer `ChildCareServices' from data source 
  `C:\Sathvika-7284\ISSS626-geo\Hands-on_Ex\Hands-on_Ex02\data\ChildCareServices.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

3. Mapping the geospatial data sets

tmap_mode('view')
tm_shape(childcare_sf)+
  tm_dots()

tmap_mode('plot')

4. Geospatial Data wrangling

4.1 Converting sf data frames to ppp class

childcare_ppp <- as.ppp(childcare_sf)

class(childcare_ppp)

[1] "ppp"

summary(childcare_ppp)

Marked planar point pattern:  1925 points
Average intensity 2.417323e-06 points per square unit

Coordinates are given to 11 decimal places

Mark variables: Name, Description
Summary:
     Name           Description       
 Length:1925        Length:1925       
 Class :character   Class :character  
 Mode  :character   Mode  :character  

Window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units
                    (33590 x 23700 units)
Window area = 796335000 square units

4.2 Creating owin object

sg_owin <- as.owin(mpsz_cl)

class(sg_owin)

[1] "owin"

plot(sg_owin)

4.3 Combining point events object and owin object

childcareSG_ppp = childcare_ppp[sg_owin]

childcareSG_ppp

Marked planar point pattern: 1925 points
Mark variables: Name, Description 
window: polygonal boundary
enclosing rectangle: [2667.54, 55941.94] x [21448.47, 50256.33] units

4.4 Clark-Evan Test for Nearest Neighbour Analysis

4.4.1 Perform the Clark-Evans test without CSR

clarkevans.test(childcareSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"))

    Clark-Evans test
    No edge correction
    Z-test

data:  childcareSG_ppp
R = 0.53532, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)

4.4.2 Perform the Clark-Evans test with CSR

clarkevans.test(childcareSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                method="MonteCarlo",
                nsim=99)

    Clark-Evans test
    No edge correction
    Monte Carlo test based on 99 simulations of CSR with fixed n

data:  childcareSG_ppp
R = 0.53532, p-value = 0.01
alternative hypothesis: clustered (R < 1)

4.5 Kernel Density Estimation Method

4.5.1 Working with automatic bandwidth selection method

kde_SG_diggle <- density(
  childcareSG_ppp,
  sigma=bw.diggle,
  edge=TRUE,
  kernel="gaussian") 

plot(kde_SG_diggle)

summary(kde_SG_diggle)

real-valued pixel image
128 x 128 pixel array (ny, nx)
enclosing rectangle: [2667.538, 55941.94] x [21448.47, 50256.33] units
dimensions of each pixel: 416 x 225.0614 units
Image is defined on a subset of the rectangular grid
Subset area = 669941961.12249 square units
Subset area fraction = 0.437
Pixel values (inside window):
    range = [-6.584123e-21, 3.063698e-05]
    integral = 1927.788
    mean = 2.877545e-06

bw <- bw.diggle(childcareSG_ppp)
bw

   sigma 
295.9712 

4.5.2 Rescalling KDE values

childcareSG_ppp_km <- rescale.ppp(
  childcareSG_ppp, 1000, "km")

kde_childcareSG_km <- density(childcareSG_ppp_km,
                              sigma=bw.diggle,
                              edge=TRUE,
                              kernel="gaussian")

plot(kde_childcareSG_km)

4.5.3 Working with different automatic badwidth methods

bw.CvL(childcareSG_ppp_km)

   sigma 
4.357209 

bw.scott(childcareSG_ppp_km)

 sigma.x  sigma.y 
2.159749 1.396455 

bw.ppl(childcareSG_ppp_km)

   sigma 
0.378997 

bw.diggle(childcareSG_ppp_km)

    sigma 
0.2959712 

kde_childcareSG.ppl <- density(childcareSG_ppp_km, 
                               sigma=bw.ppl, 
                               edge=TRUE,
                               kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG_km, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")

4.5.4 Working with different kernel methods

par(mfrow=c(2,2))
plot(density(childcareSG_ppp_km, 
             sigma=0.2959712, 
             edge=TRUE, 
             kernel="gaussian"), 
     main="Gaussian")
plot(density(childcareSG_ppp_km, 
             sigma=0.2959712, 
             edge=TRUE, 
             kernel="epanechnikov"), 
     main="Epanechnikov")
plot(density(childcareSG_ppp_km, 
             sigma=0.2959712, 
             edge=TRUE, 
             kernel="quartic"), 
     main="Quartic")
plot(density(childcareSG_ppp_km, 
             sigma=0.2959712, 
             edge=TRUE, 
             kernel="disc"), 
     main="Disc")

4.6 Fixed and Adaptive KDE

4.6.1 Computing KDE by using fixed bandwidth

kde_childcareSG_fb <- density(childcareSG_ppp_km,
                              sigma=0.6, 
                              edge=TRUE,
                              kernel="gaussian")
plot(kde_childcareSG_fb)

4.6.2 Computing KDE by using adaptive bandwidth

kde_childcareSG_ab <- adaptive.density(
  childcareSG_ppp_km, 
  method="kernel")
plot(kde_childcareSG_ab)

par(mfrow=c(1,2))
plot(kde_childcareSG_fb, main = "Fixed bandwidth")
plot(kde_childcareSG_ab, main = "Adaptive bandwidth")

4.7 Plotting cartographic quality KDE map

4.7.1 Converting gridded output into raster

kde_childcareSG_bw_terra <- rast(kde_childcareSG_km)

class(kde_childcareSG_bw_terra)

[1] "SpatRaster"
attr(,"package")
[1] "terra"

kde_childcareSG_bw_terra

class       : SpatRaster 
dimensions  : 128, 128, 1  (nrow, ncol, nlyr)
resolution  : 0.4162063, 0.2250614  (x, y)
extent      : 2.667538, 55.94194, 21.44847, 50.25633  (xmin, xmax, ymin, ymax)
coord. ref. :  
source(s)   : memory
name        :         lyr.1 
min value   : -5.824417e-15 
max value   :  3.063698e+01 
unit        :            km 

4.7.2 Assigning projection systems

crs(kde_childcareSG_bw_terra) <- "EPSG:3414"

kde_childcareSG_bw_terra

class       : SpatRaster 
dimensions  : 128, 128, 1  (nrow, ncol, nlyr)
resolution  : 0.4162063, 0.2250614  (x, y)
extent      : 2.667538, 55.94194, 21.44847, 50.25633  (xmin, xmax, ymin, ymax)
coord. ref. : SVY21 / Singapore TM (EPSG:3414) 
source(s)   : memory
name        :         lyr.1 
min value   : -5.824417e-15 
max value   :  3.063698e+01 
unit        :            km 

4.7.3 Plotting KDE map with tmap

tm_shape(kde_childcareSG_bw_terra) + 
  tm_raster(col.scale = 
              tm_scale_continuous(
                values = "viridis"),
            col.legend = tm_legend(
            title = "Density values",
            title.size = 0.7,
            text.size = 0.7,
            bg.color = "white",
            bg.alpha = 0.7,
            position = tm_pos_in(
              "right", "bottom"),
            frame = TRUE)) +
  tm_graticules(labels.size = 0.7) +
  tm_compass() +
  tm_layout(scale = 1.0)

4.8 First Order SPPA at the Planning Subzone Level

4.8.1 Geospatial data wrangling

4.8.1.1 Extracting study area

pg <- mpsz_cl %>%
  filter(PLN_AREA_N == "PUNGGOL")
tm <- mpsz_cl %>%
  filter(PLN_AREA_N == "TAMPINES")
ck <- mpsz_cl %>%
  filter(PLN_AREA_N == "CHOA CHU KANG")
jw <- mpsz_cl %>%
  filter(PLN_AREA_N == "JURONG WEST")
bk <- mpsz_cl %>%
  filter(PLN_AREA_N == "BUKIT BATOK")

par(mfrow=c(2,2))
plot(st_geometry(pg), main = "Punggol")
plot(st_geometry(tm), main = "Tampines")
plot(st_geometry(ck), main = "Choa Chu Kang")
plot(st_geometry(jw), main = "Jurong West")

plot(st_geometry(bk), main = "Bukit Batok")

4.8.1.2 Creating owin object

pg_owin = as.owin(pg)
tm_owin = as.owin(tm)
ck_owin = as.owin(ck)
jw_owin = as.owin(jw)
bk_owin = as.owin(bk)

4.8.1.3 Combining point events object and owin object

childcare_pg_ppp = childcare_ppp[pg_owin]
childcare_tm_ppp = childcare_ppp[tm_owin]
childcare_ck_ppp = childcare_ppp[ck_owin]
childcare_jw_ppp = childcare_ppp[jw_owin]
childcare_bk_ppp = childcare_ppp[bk_owin]

childcare_pg_ppp.km = rescale.ppp(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale.ppp(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale.ppp(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale.ppp(childcare_jw_ppp, 1000, "km")
childcare_bk_ppp.km = rescale.ppp(childcare_bk_ppp, 1000, "km")

par(mfrow=c(2,2))
plot(unmark(childcare_pg_ppp.km), 
  main="Punggol")
plot(unmark(childcare_tm_ppp.km), 
  main="Tampines")
plot(unmark(childcare_ck_ppp.km), 
  main="Choa Chu Kang")
plot(unmark(childcare_jw_ppp.km), 
  main="Jurong West")

plot(unmark(childcare_bk_ppp.km), 
  main="Bukit Batok")

4.8.2 Clark and Evans Test

4.8.2.1 Choa Chu Kang planning area

clarkevans.test(childcare_ck_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_ck_ppp
R = 0.84097, p-value = 0.008866
alternative hypothesis: two-sided

4.8.2.2 Tampines planning area

clarkevans.test(childcare_tm_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_tm_ppp
R = 0.66817, p-value = 6.58e-12
alternative hypothesis: two-sided

4.8.2.3 Jurong west planning area

clarkevans.test(childcare_jw_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_jw_ppp
R = 0.68968, p-value = 4.772e-10
alternative hypothesis: two-sided

4.8.2.4 Bukit Batok planning area

clarkevans.test(childcare_bk_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_bk_ppp
R = 0.8224, p-value = 0.006159
alternative hypothesis: two-sided

4.8.3 Computing KDE surfaces by planning area

par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tempines")
plot(density(childcare_ck_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Jurong West")

plot(density(childcare_bk_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Bukit Batok")

2nd Order Spatial Point Patterns Analysis Methods

1. Installing and Loading the R packages

pacman::p_load(sf, spatstat, tmap, tidyverse)

2. Second-order Spatial Point Patterns Analysis

2.1 Analysing Spatial Point Process Using G-Function

2.1.1 Choa Chu Kang planning area

2.1.1.1 Computing G-function estimation

set.seed(1234)

G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK, xlim=c(0,500))

2.1.1.2 Performing Complete Spatial Randomness Test

G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_CK.csr)

2.1.2 Tampines planning area

2.1.2.1 Computing G-function estimation

G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)

2.1.2.2 Performing Complete Spatial Randomness Test

G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_tm.csr)

2.1.3 Punggol planning area

2.1.3.1 Computing G-function estimation

G_pg = Gest(childcare_pg_ppp, correction = "best")
plot(G_pg)

2.1.3.2 Performing Complete Spatial Randomness Test

G_pg.csr <- envelope(childcare_pg_ppp, Gest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_pg.csr)

2.2 Analysing Spatial Point Process Using F-Function

2.2.1 Choa Chu Kang planning area

2.2.1.1 Computing F-function estimation

F_CK = Fest(childcare_ck_ppp)
plot(F_CK)

2.2.1.2 Performing Complete Spatial Randomness Test

F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(F_CK.csr)

2.2.2 Tampines planning area

2.2.2.1 Computing F-function estimation

F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)

2.2.2.2 Performing Complete Spatial Randomness Test

F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(F_tm.csr)

2.2.3 Punngol planning area

2.2.3.1 Computing F-function estimation

F_pg = Fest(childcare_pg_ppp, correction = "best")
plot(F_pg)

2.2.3.2 Performing Complete Spatial Randomness Test

F_pg.csr <- envelope(childcare_pg_ppp, Fest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(F_pg.csr)

2.3 Analysing Spatial Point Process Using K-Function

2.3.1 Choa Chu Kang planning area

2.3.1.1 Computing K-fucntion estimate

K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

2.3.1.2 Performing Complete Spatial Randomness Test

K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

2.3.2 Tampines planning area

2.3.2.1 Computing K-fucntion estimation

K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r, 
     ylab= "K(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

2.3.2.2 Performing Complete Spatial Randomness Test

K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(K_tm.csr, . - r ~ r, 
     xlab="d", ylab="K(d)-r", xlim=c(0,500))

2.3.3 Punngol planning area

2.3.3.1 Computing K-fucntion estimation

K_pg = Kest(childcare_pg_ppp, correction = "Ripley")
plot(K_pg, . -r ~ r, 
     ylab= "K(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

2.3.3.2 Performing Complete Spatial Randomness Test

K_pg.csr <- envelope(childcare_pg_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(K_pg.csr, . - r ~ r, 
     xlab="d", ylab="K(d)-r", xlim=c(0,500))

2.4 Analysing Spatial Point Process Using L-Function

2.4.1 Choa Chu Kang planning area

2.4.1.1 Computing L Fucntion estimation

L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

2.4.1.2 Performing Complete Spatial Randomness Test

L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

2.4.2 Tampines planning area

2.4.2.1 Computing L-fucntion estimate

L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

2.4.2.2 Performing Complete Spatial Randomness Test

L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(L_tm.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))

2.4.3 Punngol planning area

2.4.3.1 Computing L-fucntion estimate

L_pg = Lest(childcare_pg_ppp, correction = "Ripley")
plot(L_pg, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

2.4.3.2 Performing Complete Spatial Randomness Test

L_pg.csr <- envelope(childcare_pg_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(L_pg.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))